// -----------------------------
// projects/c++/primes/main.c++
// -----------------------------

/*
 To run the tests:
 % g++ -ansi -pedantic -lcppunit -ldl -Wall -DTEST main.c++ -o main.app
 % valgrind main.app
 
 To run the program:
 % g++ -ansi -pedantic -Wall main.c++ -o main.app
 % valgrind main.app < Collatz.in > Collatz.out
 
 To configure Doxygen:
 doxygen -g
 That creates the file Doxyfile.
 Make the following edits:
 EXTRACT_ALL            = YES
 EXTRACT_PRIVATE        = YES
 EXTRACT_STATIC         = YES
 GENERATE_LATEX         = NO
 
 To document the program:
 doxygen Doxyfile
 */

// --------
// includes
// --------

#include <cassert>  // assert
#include <iostream> // cin, cout, endl, ios_base, istream, ostream
//#include "PRIMES_TABLE.h"

#ifdef TEST
#include "cppunit/TestSuite.h"      // TestSuite
#include "cppunit/TextTestRunner.h" // TestRunner
#endif // TEST

// -------
// defines
// -------

#ifdef ONLINE_JUDGE
#define NDEBUG
#endif

// -------
// globals
// -------

#ifdef TEST
int PRIME_MAX = 5200000;
#else
const int PRIME_MAX = 5200000;
#endif


const int   numPrimes = 4291;
const int   PRIMES_TABLE[numPrimes] = { 
    2, 3, 5, 7, 11, 13, 17, 19,
    23, 29, 31, 37, 41, 43, 47, 53,
    59, 61, 67, 71, 73, 79, 83, 89,
    97, 101, 103, 107, 109, 113, 127, 131,
    137, 139, 149, 151, 157, 163, 167, 173,
    179, 181, 191, 193, 197, 199, 211, 223,
    227, 229, 233, 239, 241, 251, 257, 263,
    269, 271, 277, 281, 283, 293, 307, 311,
    313, 317, 331, 337, 347, 349, 353, 359,
    367, 373, 379, 383, 389, 397, 401, 409,
    419, 421, 431, 433, 439, 443, 449, 457,
    461, 463, 467, 479, 487, 491, 499, 503,
    509, 521, 523, 541, 547, 557, 563, 569,
    571, 577, 587, 593, 599, 601, 607, 613,
    617, 619, 631, 641, 643, 647, 653, 659,
    661, 673, 677, 683, 691, 701, 709, 719,
    727, 733, 739, 743, 751, 757, 761, 769,
    773, 787, 797, 809, 811, 821, 823, 827,
    829, 839, 853, 857, 859, 863, 877, 881,
    883, 887, 907, 911, 919, 929, 937, 941,
    947, 953, 967, 971, 977, 983, 991, 997,
    1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049,
    1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097,
    1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163,
    1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223,
    1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283,
    1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321,
    1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423,
    1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459,
    1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511,
    1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571,
    1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619,
    1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693,
    1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747,
    1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811,
    1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877,
    1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949,
    1951, 1973, 1979, 1987, 1993, 1997, 1999, 2003,
    2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069,
    2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129,
    2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203,
    2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267,
    2269, 2273, 2281, 2287, 2293, 2297, 2309, 2311,
    2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377,
    2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423,
    2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503,
    2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579,
    2591, 2593, 2609, 2617, 2621, 2633, 2647, 2657,
    2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693,
    2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741,
    2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801,
    2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861,
    2879, 2887, 2897, 2903, 2909, 2917, 2927, 2939,
    2953, 2957, 2963, 2969, 2971, 2999, 3001, 3011,
    3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079,
    3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167,
    3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221,
    3229, 3251, 3253, 3257, 3259, 3271, 3299, 3301,
    3307, 3313, 3319, 3323, 3329, 3331, 3343, 3347,
    3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413,
    3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491,
    3499, 3511, 3517, 3527, 3529, 3533, 3539, 3541,
    3547, 3557, 3559, 3571, 3581, 3583, 3593, 3607,
    3613, 3617, 3623, 3631, 3637, 3643, 3659, 3671,
    3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727,
    3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797,
    3803, 3821, 3823, 3833, 3847, 3851, 3853, 3863,
    3877, 3881, 3889, 3907, 3911, 3917, 3919, 3923,
    3929, 3931, 3943, 3947, 3967, 3989, 4001, 4003,
    4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057,
    4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129,
    4133, 4139, 4153, 4157, 4159, 4177, 4201, 4211,
    4217, 4219, 4229, 4231, 4241, 4243, 4253, 4259,
    4261, 4271, 4273, 4283, 4289, 4297, 4327, 4337,
    4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409,
    4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481,
    4483, 4493, 4507, 4513, 4517, 4519, 4523, 4547,
    4549, 4561, 4567, 4583, 4591, 4597, 4603, 4621,
    4637, 4639, 4643, 4649, 4651, 4657, 4663, 4673,
    4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751,
    4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813,
    4817, 4831, 4861, 4871, 4877, 4889, 4903, 4909,
    4919, 4931, 4933, 4937, 4943, 4951, 4957, 4967,
    4969, 4973, 4987, 4993, 4999, 5003, 5009, 5011,
    5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087,
    5099, 5101, 5107, 5113, 5119, 5147, 5153, 5167,
    5171, 5179, 5189, 5197, 5209, 5227, 5231, 5233,
    5237, 5261, 5273, 5279, 5281, 5297, 5303, 5309,
    5323, 5333, 5347, 5351, 5381, 5387, 5393, 5399,
    5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443,
    5449, 5471, 5477, 5479, 5483, 5501, 5503, 5507,
    5519, 5521, 5527, 5531, 5557, 5563, 5569, 5573,
    5581, 5591, 5623, 5639, 5641, 5647, 5651, 5653,
    5657, 5659, 5669, 5683, 5689, 5693, 5701, 5711,
    5717, 5737, 5741, 5743, 5749, 5779, 5783, 5791,
    5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849,
    5851, 5857, 5861, 5867, 5869, 5879, 5881, 5897,
    5903, 5923, 5927, 5939, 5953, 5981, 5987, 6007,
    6011, 6029, 6037, 6043, 6047, 6053, 6067, 6073,
    6079, 6089, 6091, 6101, 6113, 6121, 6131, 6133,
    6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211,
    6217, 6221, 6229, 6247, 6257, 6263, 6269, 6271,
    6277, 6287, 6299, 6301, 6311, 6317, 6323, 6329,
    6337, 6343, 6353, 6359, 6361, 6367, 6373, 6379,
    6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473,
    6481, 6491, 6521, 6529, 6547, 6551, 6553, 6563,
    6569, 6571, 6577, 6581, 6599, 6607, 6619, 6637,
    6653, 6659, 6661, 6673, 6679, 6689, 6691, 6701,
    6703, 6709, 6719, 6733, 6737, 6761, 6763, 6779,
    6781, 6791, 6793, 6803, 6823, 6827, 6829, 6833,
    6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907,
    6911, 6917, 6947, 6949, 6959, 6961, 6967, 6971,
    6977, 6983, 6991, 6997, 7001, 7013, 7019, 7027,
    7039, 7043, 7057, 7069, 7079, 7103, 7109, 7121,
    7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207,
    7211, 7213, 7219, 7229, 7237, 7243, 7247, 7253,
    7283, 7297, 7307, 7309, 7321, 7331, 7333, 7349,
    7351, 7369, 7393, 7411, 7417, 7433, 7451, 7457,
    7459, 7477, 7481, 7487, 7489, 7499, 7507, 7517,
    7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561,
    7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621,
    7639, 7643, 7649, 7669, 7673, 7681, 7687, 7691,
    7699, 7703, 7717, 7723, 7727, 7741, 7753, 7757,
    7759, 7789, 7793, 7817, 7823, 7829, 7841, 7853,
    7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919,
    7927, 7933, 7937, 7949, 7951, 7963, 7993, 8009,
    8011, 8017, 8039, 8053, 8059, 8069, 8081, 8087,
    8089, 8093, 8101, 8111, 8117, 8123, 8147, 8161,
    8167, 8171, 8179, 8191, 8209, 8219, 8221, 8231,
    8233, 8237, 8243, 8263, 8269, 8273, 8287, 8291,
    8293, 8297, 8311, 8317, 8329, 8353, 8363, 8369,
    8377, 8387, 8389, 8419, 8423, 8429, 8431, 8443,
    8447, 8461, 8467, 8501, 8513, 8521, 8527, 8537,
    8539, 8543, 8563, 8573, 8581, 8597, 8599, 8609,
    8623, 8627, 8629, 8641, 8647, 8663, 8669, 8677,
    8681, 8689, 8693, 8699, 8707, 8713, 8719, 8731,
    8737, 8741, 8747, 8753, 8761, 8779, 8783, 8803,
    8807, 8819, 8821, 8831, 8837, 8839, 8849, 8861,
    8863, 8867, 8887, 8893, 8923, 8929, 8933, 8941,
    8951, 8963, 8969, 8971, 8999, 9001, 9007, 9011,
    9013, 9029, 9041, 9043, 9049, 9059, 9067, 9091,
    9103, 9109, 9127, 9133, 9137, 9151, 9157, 9161,
    9173, 9181, 9187, 9199, 9203, 9209, 9221, 9227,
    9239, 9241, 9257, 9277, 9281, 9283, 9293, 9311,
    9319, 9323, 9337, 9341, 9343, 9349, 9371, 9377,
    9391, 9397, 9403, 9413, 9419, 9421, 9431, 9433,
    9437, 9439, 9461, 9463, 9467, 9473, 9479, 9491,
    9497, 9511, 9521, 9533, 9539, 9547, 9551, 9587,
    9601, 9613, 9619, 9623, 9629, 9631, 9643, 9649,
    9661, 9677, 9679, 9689, 9697, 9719, 9721, 9733,
    9739, 9743, 9749, 9767, 9769, 9781, 9787, 9791,
    9803, 9811, 9817, 9829, 9833, 9839, 9851, 9857,
    9859, 9871, 9883, 9887, 9901, 9907, 9923, 9929,
    9931, 9941, 9949, 9967, 9973, 10007, 10009, 10037,
    10039, 10061, 10067, 10069, 10079, 10091, 10093, 10099,
    10103, 10111, 10133, 10139, 10141, 10151, 10159, 10163,
    10169, 10177, 10181, 10193, 10211, 10223, 10243, 10247,
    10253, 10259, 10267, 10271, 10273, 10289, 10301, 10303,
    10313, 10321, 10331, 10333, 10337, 10343, 10357, 10369,
    10391, 10399, 10427, 10429, 10433, 10453, 10457, 10459,
    10463, 10477, 10487, 10499, 10501, 10513, 10529, 10531,
    10559, 10567, 10589, 10597, 10601, 10607, 10613, 10627,
    10631, 10639, 10651, 10657, 10663, 10667, 10687, 10691,
    10709, 10711, 10723, 10729, 10733, 10739, 10753, 10771,
    10781, 10789, 10799, 10831, 10837, 10847, 10853, 10859,
    10861, 10867, 10883, 10889, 10891, 10903, 10909, 10937,
    10939, 10949, 10957, 10973, 10979, 10987, 10993, 11003,
    11027, 11047, 11057, 11059, 11069, 11071, 11083, 11087,
    11093, 11113, 11117, 11119, 11131, 11149, 11159, 11161,
    11171, 11173, 11177, 11197, 11213, 11239, 11243, 11251,
    11257, 11261, 11273, 11279, 11287, 11299, 11311, 11317,
    11321, 11329, 11351, 11353, 11369, 11383, 11393, 11399,
    11411, 11423, 11437, 11443, 11447, 11467, 11471, 11483,
    11489, 11491, 11497, 11503, 11519, 11527, 11549, 11551,
    11579, 11587, 11593, 11597, 11617, 11621, 11633, 11657,
    11677, 11681, 11689, 11699, 11701, 11717, 11719, 11731,
    11743, 11777, 11779, 11783, 11789, 11801, 11807, 11813,
    11821, 11827, 11831, 11833, 11839, 11863, 11867, 11887,
    11897, 11903, 11909, 11923, 11927, 11933, 11939, 11941,
    11953, 11959, 11969, 11971, 11981, 11987, 12007, 12011,
    12037, 12041, 12043, 12049, 12071, 12073, 12097, 12101,
    12107, 12109, 12113, 12119, 12143, 12149, 12157, 12161,
    12163, 12197, 12203, 12211, 12227, 12239, 12241, 12251,
    12253, 12263, 12269, 12277, 12281, 12289, 12301, 12323,
    12329, 12343, 12347, 12373, 12377, 12379, 12391, 12401,
    12409, 12413, 12421, 12433, 12437, 12451, 12457, 12473,
    12479, 12487, 12491, 12497, 12503, 12511, 12517, 12527,
    12539, 12541, 12547, 12553, 12569, 12577, 12583, 12589,
    12601, 12611, 12613, 12619, 12637, 12641, 12647, 12653,
    12659, 12671, 12689, 12697, 12703, 12713, 12721, 12739,
    12743, 12757, 12763, 12781, 12791, 12799, 12809, 12821,
    12823, 12829, 12841, 12853, 12889, 12893, 12899, 12907,
    12911, 12917, 12919, 12923, 12941, 12953, 12959, 12967,
    12973, 12979, 12983, 13001, 13003, 13007, 13009, 13033,
    13037, 13043, 13049, 13063, 13093, 13099, 13103, 13109,
    13121, 13127, 13147, 13151, 13159, 13163, 13171, 13177,
    13183, 13187, 13217, 13219, 13229, 13241, 13249, 13259,
    13267, 13291, 13297, 13309, 13313, 13327, 13331, 13337,
    13339, 13367, 13381, 13397, 13399, 13411, 13417, 13421,
    13441, 13451, 13457, 13463, 13469, 13477, 13487, 13499,
    13513, 13523, 13537, 13553, 13567, 13577, 13591, 13597,
    13613, 13619, 13627, 13633, 13649, 13669, 13679, 13681,
    13687, 13691, 13693, 13697, 13709, 13711, 13721, 13723,
    13729, 13751, 13757, 13759, 13763, 13781, 13789, 13799,
    13807, 13829, 13831, 13841, 13859, 13873, 13877, 13879,
    13883, 13901, 13903, 13907, 13913, 13921, 13931, 13933,
    13963, 13967, 13997, 13999, 14009, 14011, 14029, 14033,
    14051, 14057, 14071, 14081, 14083, 14087, 14107, 14143,
    14149, 14153, 14159, 14173, 14177, 14197, 14207, 14221,
    14243, 14249, 14251, 14281, 14293, 14303, 14321, 14323,
    14327, 14341, 14347, 14369, 14387, 14389, 14401, 14407,
    14411, 14419, 14423, 14431, 14437, 14447, 14449, 14461,
    14479, 14489, 14503, 14519, 14533, 14537, 14543, 14549,
    14551, 14557, 14561, 14563, 14591, 14593, 14621, 14627,
    14629, 14633, 14639, 14653, 14657, 14669, 14683, 14699,
    14713, 14717, 14723, 14731, 14737, 14741, 14747, 14753,
    14759, 14767, 14771, 14779, 14783, 14797, 14813, 14821,
    14827, 14831, 14843, 14851, 14867, 14869, 14879, 14887,
    14891, 14897, 14923, 14929, 14939, 14947, 14951, 14957,
    14969, 14983, 15013, 15017, 15031, 15053, 15061, 15073,
    15077, 15083, 15091, 15101, 15107, 15121, 15131, 15137,
    15139, 15149, 15161, 15173, 15187, 15193, 15199, 15217,
    15227, 15233, 15241, 15259, 15263, 15269, 15271, 15277,
    15287, 15289, 15299, 15307, 15313, 15319, 15329, 15331,
    15349, 15359, 15361, 15373, 15377, 15383, 15391, 15401,
    15413, 15427, 15439, 15443, 15451, 15461, 15467, 15473,
    15493, 15497, 15511, 15527, 15541, 15551, 15559, 15569,
    15581, 15583, 15601, 15607, 15619, 15629, 15641, 15643,
    15647, 15649, 15661, 15667, 15671, 15679, 15683, 15727,
    15731, 15733, 15737, 15739, 15749, 15761, 15767, 15773,
    15787, 15791, 15797, 15803, 15809, 15817, 15823, 15859,
    15877, 15881, 15887, 15889, 15901, 15907, 15913, 15919,
    15923, 15937, 15959, 15971, 15973, 15991, 16001, 16007,
    16033, 16057, 16061, 16063, 16067, 16069, 16073, 16087,
    16091, 16097, 16103, 16111, 16127, 16139, 16141, 16183,
    16187, 16189, 16193, 16217, 16223, 16229, 16231, 16249,
    16253, 16267, 16273, 16301, 16319, 16333, 16339, 16349,
    16361, 16363, 16369, 16381, 16411, 16417, 16421, 16427,
    16433, 16447, 16451, 16453, 16477, 16481, 16487, 16493,
    16519, 16529, 16547, 16553, 16561, 16567, 16573, 16603,
    16607, 16619, 16631, 16633, 16649, 16651, 16657, 16661,
    16673, 16691, 16693, 16699, 16703, 16729, 16741, 16747,
    16759, 16763, 16787, 16811, 16823, 16829, 16831, 16843,
    16871, 16879, 16883, 16889, 16901, 16903, 16921, 16927,
    16931, 16937, 16943, 16963, 16979, 16981, 16987, 16993,
    17011, 17021, 17027, 17029, 17033, 17041, 17047, 17053,
    17077, 17093, 17099, 17107, 17117, 17123, 17137, 17159,
    17167, 17183, 17189, 17191, 17203, 17207, 17209, 17231,
    17239, 17257, 17291, 17293, 17299, 17317, 17321, 17327,
    17333, 17341, 17351, 17359, 17377, 17383, 17387, 17389,
    17393, 17401, 17417, 17419, 17431, 17443, 17449, 17467,
    17471, 17477, 17483, 17489, 17491, 17497, 17509, 17519,
    17539, 17551, 17569, 17573, 17579, 17581, 17597, 17599,
    17609, 17623, 17627, 17657, 17659, 17669, 17681, 17683,
    17707, 17713, 17729, 17737, 17747, 17749, 17761, 17783,
    17789, 17791, 17807, 17827, 17837, 17839, 17851, 17863,
    17881, 17891, 17903, 17909, 17911, 17921, 17923, 17929,
    17939, 17957, 17959, 17971, 17977, 17981, 17987, 17989,
    18013, 18041, 18043, 18047, 18049, 18059, 18061, 18077,
    18089, 18097, 18119, 18121, 18127, 18131, 18133, 18143,
    18149, 18169, 18181, 18191, 18199, 18211, 18217, 18223,
    18229, 18233, 18251, 18253, 18257, 18269, 18287, 18289,
    18301, 18307, 18311, 18313, 18329, 18341, 18353, 18367,
    18371, 18379, 18397, 18401, 18413, 18427, 18433, 18439,
    18443, 18451, 18457, 18461, 18481, 18493, 18503, 18517,
    18521, 18523, 18539, 18541, 18553, 18583, 18587, 18593,
    18617, 18637, 18661, 18671, 18679, 18691, 18701, 18713,
    18719, 18731, 18743, 18749, 18757, 18773, 18787, 18793,
    18797, 18803, 18839, 18859, 18869, 18899, 18911, 18913,
    18917, 18919, 18947, 18959, 18973, 18979, 19001, 19009,
    19013, 19031, 19037, 19051, 19069, 19073, 19079, 19081,
    19087, 19121, 19139, 19141, 19157, 19163, 19181, 19183,
    19207, 19211, 19213, 19219, 19231, 19237, 19249, 19259,
    19267, 19273, 19289, 19301, 19309, 19319, 19333, 19373,
    19379, 19381, 19387, 19391, 19403, 19417, 19421, 19423,
    19427, 19429, 19433, 19441, 19447, 19457, 19463, 19469,
    19471, 19477, 19483, 19489, 19501, 19507, 19531, 19541,
    19543, 19553, 19559, 19571, 19577, 19583, 19597, 19603,
    19609, 19661, 19681, 19687, 19697, 19699, 19709, 19717,
    19727, 19739, 19751, 19753, 19759, 19763, 19777, 19793,
    19801, 19813, 19819, 19841, 19843, 19853, 19861, 19867,
    19889, 19891, 19913, 19919, 19927, 19937, 19949, 19961,
    19963, 19973, 19979, 19991, 19993, 19997, 20011, 20021,
    20023, 20029, 20047, 20051, 20063, 20071, 20089, 20101,
    20107, 20113, 20117, 20123, 20129, 20143, 20147, 20149,
    20161, 20173, 20177, 20183, 20201, 20219, 20231, 20233,
    20249, 20261, 20269, 20287, 20297, 20323, 20327, 20333,
    20341, 20347, 20353, 20357, 20359, 20369, 20389, 20393,
    20399, 20407, 20411, 20431, 20441, 20443, 20477, 20479,
    20483, 20507, 20509, 20521, 20533, 20543, 20549, 20551,
    20563, 20593, 20599, 20611, 20627, 20639, 20641, 20663,
    20681, 20693, 20707, 20717, 20719, 20731, 20743, 20747,
    20749, 20753, 20759, 20771, 20773, 20789, 20807, 20809,
    20849, 20857, 20873, 20879, 20887, 20897, 20899, 20903,
    20921, 20929, 20939, 20947, 20959, 20963, 20981, 20983,
    21001, 21011, 21013, 21017, 21019, 21023, 21031, 21059,
    21061, 21067, 21089, 21101, 21107, 21121, 21139, 21143,
    21149, 21157, 21163, 21169, 21179, 21187, 21191, 21193,
    21211, 21221, 21227, 21247, 21269, 21277, 21283, 21313,
    21317, 21319, 21323, 21341, 21347, 21377, 21379, 21383,
    21391, 21397, 21401, 21407, 21419, 21433, 21467, 21481,
    21487, 21491, 21493, 21499, 21503, 21517, 21521, 21523,
    21529, 21557, 21559, 21563, 21569, 21577, 21587, 21589,
    21599, 21601, 21611, 21613, 21617, 21647, 21649, 21661,
    21673, 21683, 21701, 21713, 21727, 21737, 21739, 21751,
    21757, 21767, 21773, 21787, 21799, 21803, 21817, 21821,
    21839, 21841, 21851, 21859, 21863, 21871, 21881, 21893,
    21911, 21929, 21937, 21943, 21961, 21977, 21991, 21997,
    22003, 22013, 22027, 22031, 22037, 22039, 22051, 22063,
    22067, 22073, 22079, 22091, 22093, 22109, 22111, 22123,
    22129, 22133, 22147, 22153, 22157, 22159, 22171, 22189,
    22193, 22229, 22247, 22259, 22271, 22273, 22277, 22279,
    22283, 22291, 22303, 22307, 22343, 22349, 22367, 22369,
    22381, 22391, 22397, 22409, 22433, 22441, 22447, 22453,
    22469, 22481, 22483, 22501, 22511, 22531, 22541, 22543,
    22549, 22567, 22571, 22573, 22613, 22619, 22621, 22637,
    22639, 22643, 22651, 22669, 22679, 22691, 22697, 22699,
    22709, 22717, 22721, 22727, 22739, 22741, 22751, 22769,
    22777, 22783, 22787, 22807, 22811, 22817, 22853, 22859,
    22861, 22871, 22877, 22901, 22907, 22921, 22937, 22943,
    22961, 22963, 22973, 22993, 23003, 23011, 23017, 23021,
    23027, 23029, 23039, 23041, 23053, 23057, 23059, 23063,
    23071, 23081, 23087, 23099, 23117, 23131, 23143, 23159,
    23167, 23173, 23189, 23197, 23201, 23203, 23209, 23227,
    23251, 23269, 23279, 23291, 23293, 23297, 23311, 23321,
    23327, 23333, 23339, 23357, 23369, 23371, 23399, 23417,
    23431, 23447, 23459, 23473, 23497, 23509, 23531, 23537,
    23539, 23549, 23557, 23561, 23563, 23567, 23581, 23593,
    23599, 23603, 23609, 23623, 23627, 23629, 23633, 23663,
    23669, 23671, 23677, 23687, 23689, 23719, 23741, 23743,
    23747, 23753, 23761, 23767, 23773, 23789, 23801, 23813,
    23819, 23827, 23831, 23833, 23857, 23869, 23873, 23879,
    23887, 23893, 23899, 23909, 23911, 23917, 23929, 23957,
    23971, 23977, 23981, 23993, 24001, 24007, 24019, 24023,
    24029, 24043, 24049, 24061, 24071, 24077, 24083, 24091,
    24097, 24103, 24107, 24109, 24113, 24121, 24133, 24137,
    24151, 24169, 24179, 24181, 24197, 24203, 24223, 24229,
    24239, 24247, 24251, 24281, 24317, 24329, 24337, 24359,
    24371, 24373, 24379, 24391, 24407, 24413, 24419, 24421,
    24439, 24443, 24469, 24473, 24481, 24499, 24509, 24517,
    24527, 24533, 24547, 24551, 24571, 24593, 24611, 24623,
    24631, 24659, 24671, 24677, 24683, 24691, 24697, 24709,
    24733, 24749, 24763, 24767, 24781, 24793, 24799, 24809,
    24821, 24841, 24847, 24851, 24859, 24877, 24889, 24907,
    24917, 24919, 24923, 24943, 24953, 24967, 24971, 24977,
    24979, 24989, 25013, 25031, 25033, 25037, 25057, 25073,
    25087, 25097, 25111, 25117, 25121, 25127, 25147, 25153,
    25163, 25169, 25171, 25183, 25189, 25219, 25229, 25237,
    25243, 25247, 25253, 25261, 25301, 25303, 25307, 25309,
    25321, 25339, 25343, 25349, 25357, 25367, 25373, 25391,
    25409, 25411, 25423, 25439, 25447, 25453, 25457, 25463,
    25469, 25471, 25523, 25537, 25541, 25561, 25577, 25579,
    25583, 25589, 25601, 25603, 25609, 25621, 25633, 25639,
    25643, 25657, 25667, 25673, 25679, 25693, 25703, 25717,
    25733, 25741, 25747, 25759, 25763, 25771, 25793, 25799,
    25801, 25819, 25841, 25847, 25849, 25867, 25873, 25889,
    25903, 25913, 25919, 25931, 25933, 25939, 25943, 25951,
    25969, 25981, 25997, 25999, 26003, 26017, 26021, 26029,
    26041, 26053, 26083, 26099, 26107, 26111, 26113, 26119,
    26141, 26153, 26161, 26171, 26177, 26183, 26189, 26203,
    26209, 26227, 26237, 26249, 26251, 26261, 26263, 26267,
    26293, 26297, 26309, 26317, 26321, 26339, 26347, 26357,
    26371, 26387, 26393, 26399, 26407, 26417, 26423, 26431,
    26437, 26449, 26459, 26479, 26489, 26497, 26501, 26513,
    26539, 26557, 26561, 26573, 26591, 26597, 26627, 26633,
    26641, 26647, 26669, 26681, 26683, 26687, 26693, 26699,
    26701, 26711, 26713, 26717, 26723, 26729, 26731, 26737,
    26759, 26777, 26783, 26801, 26813, 26821, 26833, 26839,
    26849, 26861, 26863, 26879, 26881, 26891, 26893, 26903,
    26921, 26927, 26947, 26951, 26953, 26959, 26981, 26987,
    26993, 27011, 27017, 27031, 27043, 27059, 27061, 27067,
    27073, 27077, 27091, 27103, 27107, 27109, 27127, 27143,
    27179, 27191, 27197, 27211, 27239, 27241, 27253, 27259,
    27271, 27277, 27281, 27283, 27299, 27329, 27337, 27361,
    27367, 27397, 27407, 27409, 27427, 27431, 27437, 27449,
    27457, 27479, 27481, 27487, 27509, 27527, 27529, 27539,
    27541, 27551, 27581, 27583, 27611, 27617, 27631, 27647,
    27653, 27673, 27689, 27691, 27697, 27701, 27733, 27737,
    27739, 27743, 27749, 27751, 27763, 27767, 27773, 27779,
    27791, 27793, 27799, 27803, 27809, 27817, 27823, 27827,
    27847, 27851, 27883, 27893, 27901, 27917, 27919, 27941,
    27943, 27947, 27953, 27961, 27967, 27983, 27997, 28001,
    28019, 28027, 28031, 28051, 28057, 28069, 28081, 28087,
    28097, 28099, 28109, 28111, 28123, 28151, 28163, 28181,
    28183, 28201, 28211, 28219, 28229, 28277, 28279, 28283,
    28289, 28297, 28307, 28309, 28319, 28349, 28351, 28387,
    28393, 28403, 28409, 28411, 28429, 28433, 28439, 28447,
    28463, 28477, 28493, 28499, 28513, 28517, 28537, 28541,
    28547, 28549, 28559, 28571, 28573, 28579, 28591, 28597,
    28603, 28607, 28619, 28621, 28627, 28631, 28643, 28649,
    28657, 28661, 28663, 28669, 28687, 28697, 28703, 28711,
    28723, 28729, 28751, 28753, 28759, 28771, 28789, 28793,
    28807, 28813, 28817, 28837, 28843, 28859, 28867, 28871,
    28879, 28901, 28909, 28921, 28927, 28933, 28949, 28961,
    28979, 29009, 29017, 29021, 29023, 29027, 29033, 29059,
    29063, 29077, 29101, 29123, 29129, 29131, 29137, 29147,
    29153, 29167, 29173, 29179, 29191, 29201, 29207, 29209,
    29221, 29231, 29243, 29251, 29269, 29287, 29297, 29303,
    29311, 29327, 29333, 29339, 29347, 29363, 29383, 29387,
    29389, 29399, 29401, 29411, 29423, 29429, 29437, 29443,
    29453, 29473, 29483, 29501, 29527, 29531, 29537, 29567,
    29569, 29573, 29581, 29587, 29599, 29611, 29629, 29633,
    29641, 29663, 29669, 29671, 29683, 29717, 29723, 29741,
    29753, 29759, 29761, 29789, 29803, 29819, 29833, 29837,
    29851, 29863, 29867, 29873, 29879, 29881, 29917, 29921,
    29927, 29947, 29959, 29983, 29989, 30011, 30013, 30029,
    30047, 30059, 30071, 30089, 30091, 30097, 30103, 30109,
    30113, 30119, 30133, 30137, 30139, 30161, 30169, 30181,
    30187, 30197, 30203, 30211, 30223, 30241, 30253, 30259,
    30269, 30271, 30293, 30307, 30313, 30319, 30323, 30341,
    30347, 30367, 30389, 30391, 30403, 30427, 30431, 30449,
    30467, 30469, 30491, 30493, 30497, 30509, 30517, 30529,
    30539, 30553, 30557, 30559, 30577, 30593, 30631, 30637,
    30643, 30649, 30661, 30671, 30677, 30689, 30697, 30703,
    30707, 30713, 30727, 30757, 30763, 30773, 30781, 30803,
    30809, 30817, 30829, 30839, 30841, 30851, 30853, 30859,
    30869, 30871, 30881, 30893, 30911, 30931, 30937, 30941,
    30949, 30971, 30977, 30983, 31013, 31019, 31033, 31039,
    31051, 31063, 31069, 31079, 31081, 31091, 31121, 31123,
    31139, 31147, 31151, 31153, 31159, 31177, 31181, 31183,
    31189, 31193, 31219, 31223, 31231, 31237, 31247, 31249,
    31253, 31259, 31267, 31271, 31277, 31307, 31319, 31321,
    31327, 31333, 31337, 31357, 31379, 31387, 31391, 31393,
    31397, 31469, 31477, 31481, 31489, 31511, 31513, 31517,
    31531, 31541, 31543, 31547, 31567, 31573, 31583, 31601,
    31607, 31627, 31643, 31649, 31657, 31663, 31667, 31687,
    31699, 31721, 31723, 31727, 31729, 31741, 31751, 31769,
    31771, 31793, 31799, 31817, 31847, 31849, 31859, 31873,
    31883, 31891, 31907, 31957, 31963, 31973, 31981, 31991,
    32003, 32009, 32027, 32029, 32051, 32057, 32059, 32063,
    32069, 32077, 32083, 32089, 32099, 32117, 32119, 32141,
    32143, 32159, 32173, 32183, 32189, 32191, 32203, 32213,
    32233, 32237, 32251, 32257, 32261, 32297, 32299, 32303,
    32309, 32321, 32323, 32327, 32341, 32353, 32359, 32363,
    32369, 32371, 32377, 32381, 32401, 32411, 32413, 32423,
    32429, 32441, 32443, 32467, 32479, 32491, 32497, 32503,
    32507, 32531, 32533, 32537, 32561, 32563, 32569, 32573,
    32579, 32587, 32603, 32609, 32611, 32621, 32633, 32647,
    32653, 32687, 32693, 32707, 32713, 32717, 32719, 32749,
    32771, 32779, 32783, 32789, 32797, 32801, 32803, 32831,
    32833, 32839, 32843, 32869, 32887, 32909, 32911, 32917,
    32933, 32939, 32941, 32957, 32969, 32971, 32983, 32987,
    32993, 32999, 33013, 33023, 33029, 33037, 33049, 33053,
    33071, 33073, 33083, 33091, 33107, 33113, 33119, 33149,
    33151, 33161, 33179, 33181, 33191, 33199, 33203, 33211,
    33223, 33247, 33287, 33289, 33301, 33311, 33317, 33329,
    33331, 33343, 33347, 33349, 33353, 33359, 33377, 33391,
    33403, 33409, 33413, 33427, 33457, 33461, 33469, 33479,
    33487, 33493, 33503, 33521, 33529, 33533, 33547, 33563,
    33569, 33577, 33581, 33587, 33589, 33599, 33601, 33613,
    33617, 33619, 33623, 33629, 33637, 33641, 33647, 33679,
    33703, 33713, 33721, 33739, 33749, 33751, 33757, 33767,
    33769, 33773, 33791, 33797, 33809, 33811, 33827, 33829,
    33851, 33857, 33863, 33871, 33889, 33893, 33911, 33923,
    33931, 33937, 33941, 33961, 33967, 33997, 34019, 34031,
    34033, 34039, 34057, 34061, 34123, 34127, 34129, 34141,
    34147, 34157, 34159, 34171, 34183, 34211, 34213, 34217,
    34231, 34253, 34259, 34261, 34267, 34273, 34283, 34297,
    34301, 34303, 34313, 34319, 34327, 34337, 34351, 34361,
    34367, 34369, 34381, 34403, 34421, 34429, 34439, 34457,
    34469, 34471, 34483, 34487, 34499, 34501, 34511, 34513,
    34519, 34537, 34543, 34549, 34583, 34589, 34591, 34603,
    34607, 34613, 34631, 34649, 34651, 34667, 34673, 34679,
    34687, 34693, 34703, 34721, 34729, 34739, 34747, 34757,
    34759, 34763, 34781, 34807, 34819, 34841, 34843, 34847,
    34849, 34871, 34877, 34883, 34897, 34913, 34919, 34939,
    34949, 34961, 34963, 34981, 35023, 35027, 35051, 35053,
    35059, 35069, 35081, 35083, 35089, 35099, 35107, 35111,
    35117, 35129, 35141, 35149, 35153, 35159, 35171, 35201,
    35221, 35227, 35251, 35257, 35267, 35279, 35281, 35291,
    35311, 35317, 35323, 35327, 35339, 35353, 35363, 35381,
    35393, 35401, 35407, 35419, 35423, 35437, 35447, 35449,
    35461, 35491, 35507, 35509, 35521, 35527, 35531, 35533,
    35537, 35543, 35569, 35573, 35591, 35593, 35597, 35603,
    35617, 35671, 35677, 35729, 35731, 35747, 35753, 35759,
    35771, 35797, 35801, 35803, 35809, 35831, 35837, 35839,
    35851, 35863, 35869, 35879, 35897, 35899, 35911, 35923,
    35933, 35951, 35963, 35969, 35977, 35983, 35993, 35999,
    36007, 36011, 36013, 36017, 36037, 36061, 36067, 36073,
    36083, 36097, 36107, 36109, 36131, 36137, 36151, 36161,
    36187, 36191, 36209, 36217, 36229, 36241, 36251, 36263,
    36269, 36277, 36293, 36299, 36307, 36313, 36319, 36341,
    36343, 36353, 36373, 36383, 36389, 36433, 36451, 36457,
    36467, 36469, 36473, 36479, 36493, 36497, 36523, 36527,
    36529, 36541, 36551, 36559, 36563, 36571, 36583, 36587,
    36599, 36607, 36629, 36637, 36643, 36653, 36671, 36677,
    36683, 36691, 36697, 36709, 36713, 36721, 36739, 36749,
    36761, 36767, 36779, 36781, 36787, 36791, 36793, 36809,
    36821, 36833, 36847, 36857, 36871, 36877, 36887, 36899,
    36901, 36913, 36919, 36923, 36929, 36931, 36943, 36947,
    36973, 36979, 36997, 37003, 37013, 37019, 37021, 37039,
    37049, 37057, 37061, 37087, 37097, 37117, 37123, 37139,
    37159, 37171, 37181, 37189, 37199, 37201, 37217, 37223,
    37243, 37253, 37273, 37277, 37307, 37309, 37313, 37321,
    37337, 37339, 37357, 37361, 37363, 37369, 37379, 37397,
    37409, 37423, 37441, 37447, 37463, 37483, 37489, 37493,
    37501, 37507, 37511, 37517, 37529, 37537, 37547, 37549,
    37561, 37567, 37571, 37573, 37579, 37589, 37591, 37607,
    37619, 37633, 37643, 37649, 37657, 37663, 37691, 37693,
    37699, 37717, 37747, 37781, 37783, 37799, 37811, 37813,
    37831, 37847, 37853, 37861, 37871, 37879, 37889, 37897,
    37907, 37951, 37957, 37963, 37967, 37987, 37991, 37993,
    37997, 38011, 38039, 38047, 38053, 38069, 38083, 38113,
    38119, 38149, 38153, 38167, 38177, 38183, 38189, 38197,
    38201, 38219, 38231, 38237, 38239, 38261, 38273, 38281,
    38287, 38299, 38303, 38317, 38321, 38327, 38329, 38333,
    38351, 38371, 38377, 38393, 38431, 38447, 38449, 38453,
    38459, 38461, 38501, 38543, 38557, 38561, 38567, 38569,
    38593, 38603, 38609, 38611, 38629, 38639, 38651, 38653,
    38669, 38671, 38677, 38693, 38699, 38707, 38711, 38713,
    38723, 38729, 38737, 38747, 38749, 38767, 38783, 38791,
    38803, 38821, 38833, 38839, 38851, 38861, 38867, 38873,
    38891, 38903, 38917, 38921, 38923, 38933, 38953, 38959,
    38971, 38977, 38993, 39019, 39023, 39041, 39043, 39047,
    39079, 39089, 39097, 39103, 39107, 39113, 39119, 39133,
    39139, 39157, 39161, 39163, 39181, 39191, 39199, 39209,
    39217, 39227, 39229, 39233, 39239, 39241, 39251, 39293,
    39301, 39313, 39317, 39323, 39341, 39343, 39359, 39367,
    39371, 39373, 39383, 39397, 39409, 39419, 39439, 39443,
    39451, 39461, 39499, 39503, 39509, 39511, 39521, 39541,
    39551, 39563, 39569, 39581, 39607, 39619, 39623, 39631,
    39659, 39667, 39671, 39679, 39703, 39709, 39719, 39727,
    39733, 39749, 39761, 39769, 39779, 39791, 39799, 39821,
    39827, 39829, 39839, 39841, 39847, 39857, 39863, 39869,
    39877, 39883, 39887, 39901, 39929, 39937, 39953, 39971,
    39979, 39983, 39989, 40009, 40013, 40031, 40037, 40039,
    40063, 40087, 40093, 40099, 40111, 40123, 40127, 40129,
    40151, 40153, 40163, 40169, 40177, 40189, 40193, 40213,
    40231, 40237, 40241, 40253, 40277, 40283, 40289, 40343,
    40351, 40357, 40361, 40387, 40423, 40427, 40429, 40433,
    40459, 40471, 40483, 40487, 40493, 40499, 40507, 40519,
    40529, 40531, 40543, 40559, 40577, 40583, 40591, 40597,
    40609, 40627, 40637, 40639, 40693, 40697, 40699, 40709,
    40739, 40751, 40759, 40763, 40771, 40787, 40801, 40813,
    40819, 40823, 40829, 40841, 40847, 40849, 40853, 40867,
    40879, 40883, 40897, 40903, 40927, 40933, 40939, 40949,
    40961, 40973, 40993 };


// array of primality. O-index, so if isPrime[n] = true, then n+1 is prime
//                                 if isPrime[n] = false, then n+1 is composite
bool isPrime[PRIME_MAX]; //= { true };
int sum;
int addend[4];

// ----
// read
// ----

/**
 * reads an int into sum
 * @return true if that succeeds, false otherwise
 */
bool read (std::istream& in) {
    if (!(in >> sum))
        return false;
    return true;
}

// ---------
// nextPrime
// ---------

inline int nextPrime(int n) {
    int nextPrime = n + 1;
    for (; !isPrime[nextPrime] && nextPrime < PRIME_MAX; nextPrime++);
    
    if (nextPrime >= PRIME_MAX) return -1;
    return nextPrime;
}


// ----
// eval
// ----

/**
 * 
 */
void eval () {
    assert(sum < 10000001);
    int partialSum, i = 0;
    
    //if even
    if(sum % 2 == 0) {
        addend[0] = addend[1] = 2;
    } else {
        addend[0] = 2;
        addend[1] = 3;
    }

    partialSum = sum - addend[0] - addend[1];
    addend[2] = addend[3] = 1;
    
    while (!isPrime[addend[3]]) {
        addend[2] = nextPrime(addend[2]);
        if(addend[2] == -1) break;
        
        addend[3] = partialSum - addend[2];
        assert((addend[0] + addend[1] + addend[2] + addend[3]) == sum);
        
        //if addend[3] is bigger than PRIME_MAX, make addend[2] bigger
        while(addend[3] > PRIME_MAX) {
            addend[2] = nextPrime((partialSum/2) + i++);
            addend[3] = partialSum - addend[2];
        }
    }

    assert(isPrime[addend[0]] && isPrime[addend[1]] && isPrime[addend[2]] && isPrime[addend[3]]);
}


void loadPrimes() {
    for(int i = 2; i < numPrimes; i++)
        isPrime[i] = false;
    for(int i = numPrimes; i < PRIME_MAX; i++)
        isPrime[i] = true;
    
    for(int i = 0; i < numPrimes; i++)
        isPrime[PRIMES_TABLE[i]] = true;
}

// ----------
// findPrimes
// ----------

// array of primality: if isPrime[n] = true, then n is prime
//                     if isPrime[n] = false, then n is composite
void findPrimes() {
  int i, j;
  
    loadPrimes();
    isPrime[0] = isPrime[1] = false;
    
    //optimize by starting at 41000 in array to mark
    for (i = 41000; i < PRIME_MAX; i++) {
        // if this is composite, skip it
        if (!isPrime[i]) continue;

        // if prime, mark all multiples as composite
        for(j = i*2; j < PRIME_MAX; j+=i) {
            isPrime[j] = false;
        }
    }
}


// -----
// print
// -----

/**
 * prints the values of i, j, and v
 */
void print (std::ostream& out) {
    out << addend[0] << " " << addend[1] << " " << addend[2] << " " << addend[3] << std::endl;}

// -----
// tests
// -----

#ifdef TEST
#include "TestCollatz.h"
#endif // TEST

// ----
// main
// ----

/**
 * either runs the tests or runs the program
 */
int main () {
    using namespace std;
    ios_base::sync_with_stdio(false); // turn off synchronization with C I/O
    
#ifdef TEST
    // ----------
    // unit tests
    // ----------
    
    CppUnit::TextTestRunner tr;
    tr.addTest(TestCollatz::suite());
    tr.run();
#else
    // -------
    // program
    // -------
    
    findPrimes();

    while (read(cin)) {
        if (sum < 8) {
            cout << "Impossible." << endl;
        } else {
            eval();
            print(cout);
        }
    }

#endif // TEST
    
    return 0;
}
